A075320 Pair the odd numbers such that the k-th pair is (r, r+2k) where r is the smallest odd number not included earlier: (1, 3), (5, 9), (7, 13), (11, 19), (15, 25), (17, 29), (21, 35), (23, 39), (27, 45), ... This is the sequence of the product of the members of pairs.

3, 45, 91, 209, 375, 493, 735, 897, 1215, 1581, 1815, 2257, 2747, 3053, 3619, 3969, 4611, 5301, 5723, 6489, 6955, 7797, 8687, 9225, 10191, 11205, 11815, 12905, 13559, 14725, 15939, 16665, 17955, 19293, 20091, 21505, 22347, 23837, 25375, 26289

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Formula

a(n) = A075317(n)*A075318(n). - R. J. Mathar, Nov 12 2006

Maple

A075320 := proc(nmax) local r, k, a, pairs ; a := [3] ; pairs := [1, 3] ; k := 2 ; r := 5 ; while nops(a) < nmax do while r in pairs do r := r+2 ; od ; if r+2*k in pairs then printf("inconsistency", k) ; fi ; a := [op(a), r*(r+2*k)] ; pairs := [op(pairs), r, r+2*k] ; k := k+1 ; od ; RETURN(a) ; end: a := A075320(200) : for n from 1 to nops(a) do printf("%d, ", op(n, a)) ; od ; # R. J. Mathar, Nov 12 2006

Prog

(Python)
from math import isqrt
def A075320(n): return (m:=(n+isqrt(5*n**2)&-2)-1)*((n<<1)+m) # Chai Wah Wu, Aug 16 2022

Crossrefs

Cf. A075317, A075318, A075319.

Sequence in context: A079038 A101790 A124494 * A071968 A170921 A093585

Adjacent sequences: A075317 A075318 A075319 * A075321 A075322 A075323

Keyword

nonn

Author

Amarnath Murthy, Sep 14 2002

Extensions

More terms from R. J. Mathar, Nov 12 2006

Status

approved